MCQ
The eccentricity of the hyperbola $4{x^2} - 9{y^2} = 16$, is
- A$\frac{8}{3}$
- B$\frac{5}{4}$
- ✓$\frac{{\sqrt {13} }}{3}$
- D$\frac{4}{3}$
$a = 2,\,\,b = \frac{4}{3}$.
As we know, ${b^2} = {a^2}({e^2} - 1)$
==>$\frac{{16}}{9} = 4({e^2} - 1)$
==> ${e^2} = \frac{{13}}{9}$,
$\therefore e = \frac{{\sqrt {13} }}{3}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$S _1=\{( i , j , k ): i , j , k \in\{1,2, \ldots, 10\}\}$
$S _2=\{( i , j ): 1 \leq i < j +2 \leq 10, i , j \in\{1,2, \ldots, 10\}\},$
$S _3=\{( i , j , k , l): 1 \leq i < j < k < l, i , j , k , l \in\{1,2, \ldots ., 10\}\}$
$S _4=\{( i , j , k , l): i , j , k$ and $l$ are distinct elements in $\{1,2, \ldots, 10\}\}$
and If the total number of elements in the set $S _t$ is $n _z, r =1,2,3,4$, then which of the following statements is (are) TRUE?
$(A)$ $n _1=1000$ $(B)$ $n _2=44$ $(C)$ $n _3=220$ $(D)$ $\frac{ n _4}{12}=420$